Let the reciprocals of the roots of $5x^2 + 3x + 4$ be $\alpha$ and $\beta$. Evaluate $\alpha + \beta$.
Explanation: Denote the roots of $5x^2 + 3x +4$ by $a$ and $b$. We have that $\alpha = \frac{1}{a}$ and $\beta = \frac{1}{b}$. So, $$\alpha + \beta = \frac{1}{a} + \frac{1}{b} = \frac{a + b}{ab}.$$

Now, we know that $a + b = \frac{-3}{5}$ and $ab = \frac{4}{5}$ by the relationship between sum/products of roots and the coefficients of a polynomial.

Hence $\alpha + \beta = \dfrac{a + b}{ab} = \boxed{-\dfrac{3}{4}}$.